CIRCUIT ANALYSIS REVIEW

CIRCUITS REVIEW

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Voltage (V)

Potential difference that pushes charge through a circuit; measured in volts (V).

Current (I)

The flow of electric charge (rate of charge movement); measured in amperes (A).

Resistance (R)

Opposition to current flow; measured in ohms (Ω).

Ohm’s Law

V = I × R; relates voltage, current, and resistance in a linear circuit.

Power (P)

P = V × I; rate of energy transfer in an electrical element; units: watts (W).

Passive Sign Convention

If current enters the positive terminal of an element, power = +VI (absorbed). If it enters the negative terminal, power = –VI (delivered).

Node

A point where two or more circuit elements are connected.

Branch

A single element that connects two nodes.

Loop

A closed path through a circuit that starts and ends at the same node.

Series Connection

Elements share the same current.

Parallel Connection

Elements share the same voltage.

Kirchhoff’s Current Law (KCL)

The algebraic sum of currents entering a node equals the sum leaving it (ΣIin = ΣIout).

Kirchhoff’s Voltage Law (KVL)

The algebraic sum of voltages around any closed loop is zero (ΣV = 0).

Independent Voltage Source

Provides a fixed voltage regardless of current.

Independent Current Source

Provides a fixed current regardless of voltage.

Resistor Voltage Divider

Vout = (R2 / (R1 + R2)) × Vin; divides voltage in proportion to resistance.

Current Divider

Ibranch = (Rtotal / Rbranch) × Itotal; splits current inversely to resistance.

Equivalent Resistance (Series)

R_eq = R1 + R2 + R3 + …

Equivalent Resistance (Parallel)

1 / R_eq = 1/R1 + 1/R2 + 1/R3 + …

Nodal Analysis

Uses KCL at each node to find unknown voltages; set node equations using ΣI_out = 0.

Mesh Analysis

Uses KVL around each loop to find unknown currents; set loop equations using ΣV = 0.

Superposition Principle

For linear circuits: turn off all but one independent source, solve, and sum the effects.

Source Transformation

A voltage source in series with a resistor ↔ equivalent current source in parallel with same resistor (V = I × R).

Thevenin Equivalent

A network replaced by a single voltage source (Vth) and resistor (Rth) seen from two terminals.

Norton Equivalent

A network replaced by a single current source (In) and resistor (Rn) seen from two terminals (In = Vth / R_th).

Open-Circuit Voltage (V_th)

Voltage across terminals when no load is connected.

Short-Circuit Current (I_n)

Current through terminals when shorted.

Maximum Power Transfer

The load gets maximum power when Rload = Rth.

Dependent (Controlled) Source

A source whose value depends on a voltage or current elsewhere in the circuit.

Voltage-Controlled Voltage Source (VCVS)

V = μVx; output voltage proportional to controlling voltage.

Current-Controlled Voltage Source (CCVS)

V = rIx; output voltage proportional to controlling current.

Voltage-Controlled Current Source (VCCS)

I = gVx; output current proportional to controlling voltage.

Current-Controlled Current Source (CCCS)

I = βIx; output current proportional to controlling current.

Controlling Variable

The voltage or current that determines the dependent source’s output.

Linear Circuit

A circuit made of elements (resistors, sources) that obey superposition and homogeneity.

Op-Amp

A high-gain voltage amplifier with differential input and single-ended output.

Ideal Op-Amp Rules

Input current = 0; voltage difference between inputs = 0 (V+ = V− in negative feedback).

Inverting Amplifier

Output voltage = −(Rf / Rin) × V_in.

Non-Inverting Amplifier

Output voltage = (1 + Rf / Rin) × V_in.

Voltage Follower (Buffer)

Output follows input (gain = 1); high input impedance, low output impedance.

Summing Amplifier

Output = −Rf × (V1/R1 + V2/R2 + …).

Difference Amplifier

Output = (R2/R1) × (V2 − V1).

Comparator

Op-amp without feedback; output switches high/low depending on which input is greater.

Negative Feedback

Feeds part of the output back to the inverting input to stabilize gain and linearize response.

Short Circuit

Zero resistance path; voltage across = 0 V.

Open Circuit

Infinite resistance; current through = 0 A.

Equivalent Circuit

Simplified version of a complex network preserving external behavior.

Linearity

A property allowing the use of superposition and proportionality.

Power Absorbed

Positive when current enters the positive terminal.

Power Delivered

Negative when current enters the negative terminal (source supplying energy).

DC Source

Constant with time (steady value).

AC Source

Time-varying (usually sinusoidal).

Ground Reference

Common node with 0 V reference potential.

Dependent vs. Independent

Dependent: controlled by another circuit variable; Independent: fixed value.

Active vs. Passive Element

Active: can deliver power (source); Passive: only absorbs (resistor).

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